"The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat's Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding."
That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math?
I suggest if one looks at the history of funding for mathematics and science, the product of these efforts is not understanding, but rather power. Funding went way up after WW2 when the war demonstrated that power flows from them. Math not only contributed to the scientific weapons of the way, but was directly used in operation planning (the birth of the field of Operations Research) as well as in cryptography.
The reason this matters is that AI is also a quintessential power-oriented technology. From the point of those providing the monetary lifeblood on which modern mathematical practice depends, the current math-AI discussion presents no issue worthy of concern.
There is more to math, than input (money) and output (power). Sure, there is some relation between applied sciences and how knowlegde can assist effecting world events.
But for the most part, math discovery relied more on human curiosity than on resources to "do math". Conversely, if people allocate lots of money to developing AI, that doesn't mean mathematicians have an obligation to take the money provide ROI to investors.
> Terence Tao - Professor, University of California, Los Angeles
> This has been the result of months of community input about the fundamental values and goals of the mathematical community. In retrospect, these were questions we should have been systematically discussing years ago, but in any event the exercise was extremely valuable, and the end result is excellent. I wholeheartedly endorse the statements and recommendations in this declaration.
>I support this declaration. I have one small comment: the document notes that "Technologies which affect the way in which mathematics is practiced may disturb the current system of incentives." The current system of incentives seriously is flawed in many ways, and I don't think maintaining the status quo should be our goal. However, we should work to improve it, not let it be corrupted by outside forces, as has already been done for decades by university administrators, journal oligopolies, etc.
yes, that's where a conference was held that kickstarted the group that drafted this declaration.
> In September 2025 the Lorentz Center at Leiden University in the Netherlands hosted a conference entitled Mechanization and Mathematical Research. The around 60 participants from 10 countries comprised mathematicians, computer scientists, philosophers, historians and social scientists, including those with experience in industry and in government.
The potential threats section reads like panic, rather than a critique of AI. I can see where #2 has some legs, if I thought tradition was sacrosanct.
1. AI proofs might be incorrect and difficult to demonstrate why. This implies they are not like human proofs in these qualities.
2. AI proofs are difficult to attribute correctly, because they don't follow established traditions. Nothing to do with the math, but ok.
3. Mathematicians without AI (for political or practical reasons) will not necessarily be able to participate in AI-assisted research. This history of Mathematics is littered with people having uneven access.
4. People/orgs are publishing that AI found things are fact before they are properly evaluated. Same issue.
5. All these things are bad, because AI might muddy the field with lots of unknowns.
This appears to be a very bad faith post that intentionally misrepresents what is being said.
1. pertains to the quantity of output adding stress to review processes; LLMs can feasibly produce a million plausible but incorrect 'proofs' in the time that a human can produce one. We already see this effect in software development, with bug bounty programs shutting down and open-source software rejecting AI contributions or closing altogether because LLMs flood review channels with an amount of spam for which there is no sufficient amount of human bandwidth to handle.
2. is nothing about "following established traditions" but rather the general concept of crediting people for their prior work, unless you think that "not plagiarising" is a trifling established tradition.
3. is more or less accurate to the point they made, but "it has historically been this way" isn't a compelling justification for "it should always be this way and also it's okay if it gets worse"
4. An existing issue being made 100x more common is a point worth bringing attention to even if it already existed, actually
5. said nothing that could possibly be interpreted in the vein of "muddying the field with lots of unknowns" at all. Point 5 was actually about economic incentives and the risk of mathematic research becoming beholden to tech monopolies
The actual thesis of point 2 is about plagiarism, and the thesis would remain the same if the sentence you quoted were removed completely. Your portrayal of it moves the out-of-context snippet to the forefont of the argument and makes it sound like an issue of "tradition for tradition's sake" or something similarly indefensible, but you refuse to engage with the real argument being made, hence why I suspect you are acting in bad faith. Are you suggesting that not attributing credit to work you've copied from is the way things should be going forward? If you are, then argue that point and make it earnestly. Instead you continue to avoid any substantial discussion of the points raised and only went for a cheap "gotcha".
It's worth remembering Thurston's essay on mathoverflow (https://mathoverflow.net/questions/43690/whats-a-mathematici...):
"The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat's Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding."
That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math?
I suggest if one looks at the history of funding for mathematics and science, the product of these efforts is not understanding, but rather power. Funding went way up after WW2 when the war demonstrated that power flows from them. Math not only contributed to the scientific weapons of the way, but was directly used in operation planning (the birth of the field of Operations Research) as well as in cryptography.
The reason this matters is that AI is also a quintessential power-oriented technology. From the point of those providing the monetary lifeblood on which modern mathematical practice depends, the current math-AI discussion presents no issue worthy of concern.
There is more to math, than input (money) and output (power). Sure, there is some relation between applied sciences and how knowlegde can assist effecting world events.
But for the most part, math discovery relied more on human curiosity than on resources to "do math". Conversely, if people allocate lots of money to developing AI, that doesn't mean mathematicians have an obligation to take the money provide ROI to investors.
> Terence Tao - Professor, University of California, Los Angeles
> This has been the result of months of community input about the fundamental values and goals of the mathematical community. In retrospect, these were questions we should have been systematically discussing years ago, but in any event the exercise was extremely valuable, and the end result is excellent. I wholeheartedly endorse the statements and recommendations in this declaration.
John Carlos Baez:
>I support this declaration. I have one small comment: the document notes that "Technologies which affect the way in which mathematics is practiced may disturb the current system of incentives." The current system of incentives seriously is flawed in many ways, and I don't think maintaining the status quo should be our goal. However, we should work to improve it, not let it be corrupted by outside forces, as has already been done for decades by university administrators, journal oligopolies, etc.
(Leiden being the town in the Netherlands where Leiden University is.)
Arguably the most beautiful town in the Netherlands
Beautiful area. I lived there for a time during the pandemic and I really enjoyed walking the canals.
1. first they ignore you <<<< GPT-4 can barely add too numbers without making a mistake
2. then they laugh at you <<<< the International Math Olympiad is basically just high school math
3. then they fight you <<<< this declaration
4. then you win
> add too numbers Did you do this on purpose to anger both Mathematicians and keen spellers?
4. then you write empty cliches
Is there a connection to Leiden, NL?
These type of questions are the reason why LLMs will take your job :-)
yes, that's where a conference was held that kickstarted the group that drafted this declaration.
> In September 2025 the Lorentz Center at Leiden University in the Netherlands hosted a conference entitled Mechanization and Mathematical Research. The around 60 participants from 10 countries comprised mathematicians, computer scientists, philosophers, historians and social scientists, including those with experience in industry and in government.
The potential threats section reads like panic, rather than a critique of AI. I can see where #2 has some legs, if I thought tradition was sacrosanct.
1. AI proofs might be incorrect and difficult to demonstrate why. This implies they are not like human proofs in these qualities.
2. AI proofs are difficult to attribute correctly, because they don't follow established traditions. Nothing to do with the math, but ok.
3. Mathematicians without AI (for political or practical reasons) will not necessarily be able to participate in AI-assisted research. This history of Mathematics is littered with people having uneven access.
4. People/orgs are publishing that AI found things are fact before they are properly evaluated. Same issue.
5. All these things are bad, because AI might muddy the field with lots of unknowns.
This appears to be a very bad faith post that intentionally misrepresents what is being said.
1. pertains to the quantity of output adding stress to review processes; LLMs can feasibly produce a million plausible but incorrect 'proofs' in the time that a human can produce one. We already see this effect in software development, with bug bounty programs shutting down and open-source software rejecting AI contributions or closing altogether because LLMs flood review channels with an amount of spam for which there is no sufficient amount of human bandwidth to handle.
2. is nothing about "following established traditions" but rather the general concept of crediting people for their prior work, unless you think that "not plagiarising" is a trifling established tradition.
3. is more or less accurate to the point they made, but "it has historically been this way" isn't a compelling justification for "it should always be this way and also it's okay if it gets worse"
4. An existing issue being made 100x more common is a point worth bringing attention to even if it already existed, actually
5. said nothing that could possibly be interpreted in the vein of "muddying the field with lots of unknowns" at all. Point 5 was actually about economic incentives and the risk of mathematic research becoming beholden to tech monopolies
I'm not sure it's constructive to explain our differences, point by point. eg
> 2. is nothing about "following established traditions"
> undermine the traditional system of attribution
Literally does.
Suffice to say, I find your interpretations to be surprising and disconnected and it has not changed my views.
The actual thesis of point 2 is about plagiarism, and the thesis would remain the same if the sentence you quoted were removed completely. Your portrayal of it moves the out-of-context snippet to the forefont of the argument and makes it sound like an issue of "tradition for tradition's sake" or something similarly indefensible, but you refuse to engage with the real argument being made, hence why I suspect you are acting in bad faith. Are you suggesting that not attributing credit to work you've copied from is the way things should be going forward? If you are, then argue that point and make it earnestly. Instead you continue to avoid any substantial discussion of the points raised and only went for a cheap "gotcha".